Objectives

State the difference
in cause and effect of random and systematic errors.

State two ways to reduce
errors in an experiment.

Know where the units of
time came from.

Know
how to pick appropriately sized units for measuring something.

Know the difference
between basic units and secondary units based on them.

State an operational
definition of speed.

This section addresses, in
whole or in part, the following Georgia GPS standard(s):

S8P3. Students will investigate relationship between force, mass, and
the motion of objects.

S8CS3. Students will have the computation and
estimation skills necessary for analyzing data and following
scientific explanations.
a. Analyze scientific data by using, interpreting, and
comparing numbers in several equivalent forms, such as integers,
fractions, decimals, and percents. b. Find the mean, median, and mode and use them to analyze a set of
scientific data. c. Apply the metric system to scientific investigations that include
metric to metric conversions (i.e., centimeters to meters). d. Decide what degree of precision is adequate, and round off
appropriately. e. Address the relationship between accuracy and precision.
f. Use ratios and proportions, including constant rates, in appropriate
problems.

S8CS4. Students will use tools and instruments for
observing, measuring, and manipulating equipment and materials
in scientific activities utilizing safe laboratory procedures.
a. Use appropriate technology to store and retrieve
scientific information in topical, alphabetical, numerical, and
keyword files, and create simple files.
b. Use appropriate tools and units for measuring objects
and/or substances.
c. Learn and use standard safety practices when conducting
scientific investigations.

This section addresses, in
whole or in part, the following Benchmarks for Scientific Literacy:

Almost anything has limits on
how big or small it can be.

Finding out what the biggest
and the smallest possible values of something are is often as
revealing as knowing what the usual value is.

Things in nature and things
people make have very different sizes, weights, ages, and speeds.

Estimate distances and travel
times from maps and the actual size of objects from scale drawings.

Determine what unit (such as
seconds, square inches, or dollars per tankful) an answer should be
expressed in from the units of the inputs to the calculation, and be
able to convert compound units (such as yen per dollar into dollar
per yen, or miles per hour into feet per second).

This section addresses, in
whole or in part, the following National Science Education Standards:

Tools help scientists make better observations, measurements,
and equipment for investigations. They help scientists see, measure,
and do things that they could not otherwise see, measure, and do.

Scientists rely on technology to enhance the gathering and
manipulation of data. New techniques and tools provide new evidence
to guide inquiry and new methods to gather data, thereby
contributing to the advance of science. The accuracy and precision
of the data, and therefore the quality of the exploration, depends
on the technology used.

“Are we there yet??” - The
need to measure

This ancient wail, whether
from the back seat of that aged Chevrolet or the back of an ancient Roman
chariot, expresses the primal need that even non-scientists will recognize -
the need to measure.

The most common measures are
those of distance and time. These two measures are separate, and
yet intricately linked. With these two items, together and apart, we determine
our place. It isn’t called the space-time continuum in Star Trek, or physics,
simply because it rolls off the tongue so well.

Vocabulary

Measurement

Origin

Positive Direction

Unit

Random Error

Systematic Error

Units of Time: Eon, Year,
Month, Week, Day, Hour, Minute, Second

Units of Distance:
Astronomical Unit, miles, meters, kilometers.

Metric

Speed

The Science of Measurement

Measurement is the second
level up from the most basic level of scientific observation. Anyone can
observe a planet, a sunset, the road ahead, the day just past, and give a
description of it. But to know it better, one must determine its
extent and limits, and how that connects with other extended and limited its.

These require some
quantitative way of assessing it, something other than general
appearances (which is qualitative in nature).

Quantitative requires a
system of measures.

Science needs measures. It’s
the starting point and sometimes the end point.

Sometimes it is the item that
supports a new theory, sometimes theory and measurement don’t agree— and out
goes the theory.

The measurement is all but
sacred. And yet…

All measurements do have four
things in common:

1.You
have to have a starting point or origin.

Where’s zero?

It can be quite arbitrary where
zero is but you have to have one somewhere.

On the highway, zero can be the
southern or western boundary of the county, or the state line. It could start
from the northern or eastern side, if we wanted to.

But once we all agree (or
somebody stronger than you says so), that’s where the zero is.

Most rulers have zero on the
left end. It doesn’t have to be. But zero DOES have to BE…somewhere.

2.You
have to have a positive direction.

Which way do we go to get to 1,
or a hundred?

Left, right, up, down, along
the incline, around the circle clockwise (and what is clockwise anyway, who
decided that?), radially away from the center —

Some direction has to be
declared to be the way the measurement increases.

In some cases, nature suggests
a ‘logical’ way (clockwise for one, it’s the way the shadow moves on a sundial,
the first clocks).

Sometimes it’s
arbitrary—azimuth increases to the east instead of to the west.

Again, sometimes these seem to
follow a natural path, other times it comes from some quirk of a human.

4.Finally,
no measurement ever made is perfect.

There is no absolutely precise
measurement.

You can never get infinitely
accurate because no measuring device can do it, and human frailties never go
away either.

All measurements are some
number X plus or minus some (hopefully very small!) Y.

And if you change your origin
or scale or just use a ruler that was made systematically larger than it should,
your measurements will change as well.

Use a different reference
framework and you can literally go from zero to infinity in no time at all.

You are sitting here at the
computer reading; but sitting is saying you have no measurement of speed
compared to the computer, which is true. It is also true that you are moving
just under 1000 miles per hour around the Earth’s axis and nearly at the speed
of light compared to a galaxy at the far end of the universe. All it took was
to change from where you are referencing your measurements.

Part of the history of
science has been the refinement of measurements.

How big exactly is one
meter?

Where is the Earth located in
reference to the center of the universe?

Where IS the center of the
universe (flipped around, where’s the edge of the universe so we can determine
the center!)?

(If you don’t think accurate
measurements are important - accurate in origin point, positive direction,
most precision, and proper units - just ask the NASA engineers who lost a Mars
probe a few years ago because they didn’t convert between feet and meters on a
crucial command to the probe!!)

Time and Distance

The two most common
measurements are those of time and distance.

There are many units for
each.

What is the amount of
distance for a distance of “one”? That depends on what units you want.

One meter is the metric
standard unit but it’s one ten-millionth of the distance from the equator to the
pole through Paris.

One astronomical unit is the
measurement used for distances in the solar system; it’s also about 93,000,000
miles or 149,000,000 kilometers.

All distances can be used
interchangeably with some mathematical conversion formulae but some are more
convenient than others.

Would you tell that "Wailing
Willy" in the back of Chevy it is only 23,459 meters to Grandma’s house?
Wouldn’t “about 23 and half kilometers” work better? Well, probably not unless
the child was raised in a house of American scientists or almost any other
country in the world that uses metrics!

Wailing Willy is more used to short
distances, like feet and inches, rather than miles and kilometers.

But he does have some
understanding of time. Time is pretty standardized.

Seconds, minutes, hours,
days, weeks, years. Notice I left out months.

But there are different
definitions of seconds going back to the dim mists of history and forward to
atomic oscillations.

On the other end, the Earth
is but a "mere" 4.5 billion years old.

Months came about from the
time it takes for our moon to change its shape.

That’s different from the
‘month’ it takes to actually orbit the Earth.

Year units actually depend on
whether you are measuring the Sun’s actual motion against the stars, or motion
taking into account the slightly precessional motion of the Earth’s orbit, or
where the closest point to the Sun points to during consecutive years,
or….hopefully you get the idea.

And maybe time isn’t so
standardized after all.

Bottom line is….pick the
units that are most convenient (generally comparable in size to the thing being
measured). And remember to be as precise as you can, but be aware that
you can’t be infinitely precise.

Measurements in Science
Experiments

When scientists make
measurements in experiments or studies, the measurements are made more
accurate by one of two similar ways.

The ONE way is making more
and more measurements. The DIFFERENCE is either the scientists makes many
measurements over and over again himself, or gets many other people to make
measures. The reason is that if you make many measurements, your final average
of them will be much closer to the real answer (whatever that is) than any
individual measures.

Remember that each measure
has some uncertainty in it due to measuring device inaccuracies and
humanity’s imperfect perception abilities.

Any individual measurement
can be close or far but there’s no way to tell. But measure a lot and the
answers tend to fall around a mean value, which may still be off but a whole lot
closer than the individual measures.

This is called random
error and it can be made as small as possible but never eliminated.
This is where the plus and minus part comes in.

There is another form
of measurement problem called systematic error.

You measure the sun’s
diameter, and measure and measure…and your final answer is 10% higher than it
should be. Why?

Perhaps your measuring device
is heat sensitive and the scale expanded 10% so all the lengths are 10% bigger
than they should be.

Perhaps the scale is fine but
you always, even unconsciously, take your reading a bit to the right of the
black marks on the scale.

How do you know if you are ON
the scale mark anyway? That 10 cm line on the meter stick isn’t infinitely
thin; is 10 cm on left or right edge or in the middle of the black line?

Maybe the manufacturer put the scale on 5 mm to far to the right?

Maybe the zero
end of the meter stick has been worn off a little so that the end is now at 2 mm. All your measures will be 2 mm
off.

All these contribute to
measures being systematically over- or under-estimated.

Wailing Willy may like it if your
time sense is so off that “we’ll be there in five minutes” turns out to be
really 20 minutes.

Systematic errors can be
eliminated, through calibrations, through changes of measuring origins
and directions (measure from the left, measure from the right, average them
together, fight fight fight! Sorry….mathematicians cheer…), using other
measuring devices (3 different spectroscopes), and so on.

Speed

There are units of
measurements…..and there are new units built on the base units. There is
nothing more basic than time and length, say seconds and meters. But if you
combine them, you get new units. Measure the distance between two places in
meters, start from A and go to B. Now run back to A and measure how many
seconds it takes to get back. Divide the distance by the time and you
get…..speed! New unit: meters per second. This is the unit for speed, a
measure of how fast something is going (in this case, you).

Not good enough? Start at
the Sun (ouch!) and follow a light beam to the Earth. How far? (1 astronomical
unit or 93,000,000 miles, or….) How long did it take? (About 500 seconds).
Speed? Wellll, you could go 93,000,000 divided by 500 and about 25,000 miles
per second, another unit of speed. But how about 8.3 light-seconds? That’s how
long it takes light to travel from there to here but we’ve turned it into a unit
of distance! See, speed and distance and time are all linked. You can’t get
the first at all unless you have the last two.

As you progress through the
sciences you will find many other units of measurements. Some quite basic but
most are somewhere, somehow based on more primitive units. The former are called
derived units. They are derived as combinations ultimately based upon the seven
Basic Units, of which time and length are two.

Units of Measure

Below is a web page with many units of
measures you can check out, including some of historical interest.
It can be perused by system (UK, American, metric, more), what they
measure (length, heat, force, etc.), and extra stuff, like those
pesky, Greek-sounding prefixes for bigger and smaller amounts of
each unit.

There are at least two ways to reduce the
size of random error. What are they?

What is the origin of the week?

List what units would be appropriate….and
inappropriate for measuring the length of a table top side. Explain
why.

What is the difference between basic units
and secondary units, and name examples.

State an operational definition of speed.

Define

Measurement

Origin

Positive Direction

Metric

Speed

A Problem

A Georgia science teacher
wins a free trip to Los Angeles, California. It takes her 50,756 seconds to
make the trip. Using a ruler and map with a distance scale, determine how far
it is to Los Angeles in miles, and then determine: